Question

Find the measure of the exterior angles of the regular pentagon using the polygon Exterior Angle Sum Theorem

Answer 1

The Polygon Exterior Angle Sum Theorem states that the sum of the exterior angles of any polygon is always \(360^\circ\), regardless of the number of sides.

For a regular polygon, the measure of each exterior angle can be calculated by dividing the total sum of the exterior angles by the number of sides.

A regular pentagon has 5 sides. Therefore, we can find the measure of each exterior angle as follows:

\[
\text{Measure of each exterior angle} = \frac{\text{Sum of exterior angles}}{\text{Number of sides}} = \frac{360^\circ}{5}
\]

Calculating this gives:

\[
\text{Measure of each exterior angle} = \frac{360^\circ}{5} = 72^\circ
\]

Thus, the measure of each exterior angle of a regular pentagon is \(72^\circ\).